Information on Result #1316278
Linear OA(25631, 783, F256, 18) (dual of [783, 752, 19]-code), using 7 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0) based on linear OA(25630, 775, F256, 18) (dual of [775, 745, 19]-code), using
- construction XX applied to C1 = C([121,137]), C2 = C([120,136]), C3 = C1 + C2 = C([121,136]), and C∩ = C1 ∩ C2 = C([120,137]) [i] based on
- linear OA(25628, 771, F256, 17) (dual of [771, 743, 18]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {121,122,…,137}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25628, 771, F256, 17) (dual of [771, 743, 18]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {120,121,…,136}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25630, 771, F256, 18) (dual of [771, 741, 19]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {120,121,…,137}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25626, 771, F256, 16) (dual of [771, 745, 17]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {121,122,…,136}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code) (see above)
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25631, 783, F256, 2, 18) (dual of [(783, 2), 1535, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25631, 783, F256, 3, 18) (dual of [(783, 3), 2318, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(25631, 783, F256, 4, 18) (dual of [(783, 4), 3101, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(25631, 783, F256, 5, 18) (dual of [(783, 5), 3884, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(25631, 783, F256, 6, 18) (dual of [(783, 6), 4667, 19]-NRT-code) | [i] | ||
| 6 | Digital (13, 31, 783)-net over F256 | [i] | ||